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Romanian Masters of Mathematics Collection
2021 Romanian Master of Mathematics Shortlist
A1
A1
Part of
2021 Romanian Master of Mathematics Shortlist
Problems
(1)
Exercisable functional equation
Source: RMM Extralist 2021 A1
9/18/2023
Determine all functions
f
:
R
ā
R
f:\mathbb{R} \to \mathbb{R}
f
:
R
ā
R
such that
f
(
x
y
+
f
(
x
)
)
+
f
(
y
)
=
x
f
(
y
)
+
f
(
x
+
y
)
f(xy+f(x)) + f(y) = xf(y) + f(x+y)
f
(
x
y
+
f
(
x
))
+
f
(
y
)
=
x
f
(
y
)
+
f
(
x
+
y
)
for all real numbers
x
x
x
and
y
y
y
.
RMM Shortlist
algebra
functional equation
substitutions
function